The sixth status, requires_escalation, means the session "requires information that cannot be provided via API, or buyer input is required".
In that case the business "MUST provide continue_url", and it must include at least one message with one of two severities:
requires_buyer_input: "Business requires input not available via API".
requires_buyer_review: "Buyer review and authorization is required".
For both, the platform's action is the same: hand off via continue_url. The platform should first resolve any errors it can fix itself, and then send the buyer to that address.
The continue_url "enables checkout handoff from platform to business UI, allowing the buyer to continue and finalize the checkout session". It must be an absolute HTTPS URL and should preserve the checkout state, so the buyer arrives on your checkout with what the agent already set up. The specification says a business should provide a continue_url for the other unfinished statuses too, and should leave it out once a checkout is completed or canceled.
Escalation can come up at more than one point. The state chart links requires_escalation to incomplete, and a Complete request can itself come back with requires_escalation for a buyer hand-off. That is why the sequence figure draws the escalation case apart from the main path. The state chart draws the hand-off at continue_url ending in completed. The text does not say whether the agent hears back, or how.
The checkout specification states near its start: "The checkout has to be finalized manually by the user through a trusted UI unless the AP2 Mandates extension is supported." Read as written, by default a person confirms the purchase in an interface they trust. An agent finishing a purchase on its own depends on the store supporting the AP2 Mandates extension.